The 24-hour rule is a U.S. Department of Transportation requirement that airlines either hold a reservation at the quoted fare without payment, or let you cancel it without penalty, for at least 24 hours after you make it, as long as you book at least one week before the flight departs. Airlines can choose which of the two options to offer; they do not have to offer both.
The rule applies to U.S. airlines and to foreign airlines on flights to and from the United States that use aircraft with 30 or more seats. When a refund is due, the airline must return the money in the original form of payment and may not keep a processing fee. The rule covers bookings made with the airline itself, so tickets bought through an online travel agency follow that agency’s own policy.
Source: eCFR: 14 CFR 259.5, Customer Service Plan
Image: Departures board at Miami International Airport, photo by Bobby Hidy, CC BY-SA 2.0, via Wikimedia Commons.